Because of the enforced zero due to point-mass prior, a blocked Gibbs sampler for sampling covariance matrix from the resulting posterior or reversible jump MCMC (RJMCMC) for computing posterior model probabilities of covariance structures is not suitable in this case. To be specific, the enforced zero due to point-mass makes it difficult to derive conditional posteriors induced from the proposed prior if one considers the blocked Gibbs sampler proposed by [1]}, hence bthe locked Gibbs sampler is not applicable to this case. Furthermore, if point-mass is introduced, there are \(2^{\binom{p}{2}}\)  models that RJMCMC has to visit over, which makes practical implementation extremely difficult as \(p\)  grows and the estimated posterior model probability of the covariance structure unreliable. We show that the error by Laplace approximation becomes asymptotically marginal at some rate depending on the posterior convergence rate of covariance matrix under the Frobenius norm.
